M. G. Magomed-Kasumov, T. N. Shakh-Emirov, “On the Representation of Sobolev Systems Orthogonal with Respect to the Inner Product with One Discrete Point”, Mat. Zametki, 2022, Volume 111, Issue 4,Pages <nobr>561

On the Representation of Sobolev Systems Orthogonal with Respect to the Inner Product with One Discrete Point

M. G. Magomed-Kasumov^ab, T. N. Shakh-Emirov^b

^a Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz
^b Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala

Abstract: We obtain the representation of systems of functions $\Phi_1$ orthogonal with respect to the Sobolev-type inner product with one discrete point in terms of functions of systems orthogonal in $L^2$. Questions relating to the completeness of the system $\Phi_1$ are investigated. Some properties of systems of functions obtained by differentiating the system $\Phi_1$ are studied.

Keywords: Sobolev orthogonality, completeness of orthogonal systems, representation of Sobolev systems, differentiation of Sobolev systems.

UDC: 517.538

Received: 11.10.2021
Revised: 24.11.2021

DOI: 10.4213/mzm13321